Skip to main content
    • Aa
    • Aa

Stall onset on aerofoils at low to moderately high Reynolds number flows

  • Wallace J. Morris (a1) and Zvi Rusak (a1)

The inception of leading-edge stall on stationary, two-dimensional, smooth, thin aerofoils at low to moderately high chord Reynolds number flows is investigated by a reduced-order, multiscale model problem via numerical simulations. The asymptotic theory demonstrates that a subsonic flow about a thin aerofoil can be described in terms of an outer region, around most of the aerofoil’s chord, and an inner region, around the nose, that asymptotically match each other. The flow in the outer region is dominated by the classical thin aerofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number $(R{e}_{M} )$ are used to correctly account for the nonlinear behaviour and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model problem of a uniform, incompressible and viscous flow past a semi-infinite parabola with a far-field circulation governed by a parameter $\tilde {A} $ that is related to the aerofoil’s angle of attack, nose radius of curvature, thickness ratio, and camber. The model flow problem is solved for various values of $\tilde {A} $ through numerical simulations based on the unsteady Navier–Stokes equations. The value ${\tilde {A} }_{s} $ where a global separation zone first erupts in the nose flow, accompanied by loss of peak streamwise velocity ahead of it and change in shedding frequency behind it, is determined as a function of $R{e}_{M} $ . These values indicate the stall onset on the aerofoil at various flow conditions. It is found that ${\tilde {A} }_{s} $ decreases with $R{e}_{M} $ until some limit $R{e}_{M} $ ( ${\sim }300$ ) and then increases with further increase of Reynolds number. At low values of $R{e}_{M} $ the flow is laminar and steady, even when stall occurs. The flow in this regime is dominated by the increasing effect of the adverse pressure gradient, which eventually overcomes the ability of the viscous stress to keep the boundary layer attached to the aerofoil. The change in the nature of stall at the limit $R{e}_{M} $ is attributed to the appearance of downstream travelling waves in the boundary layer that shed from the marginal separation zone and grow in size with either $\tilde {A} $ or $R{e}_{M} $ . These unsteady, convective vortical structures relax the effect of the adverse pressure gradient on the viscous boundary layer to delay the onset of stall in the mean flow to higher values of ${\tilde {A} }_{s} $ . Computed results show agreement with marginal separation theory at low $R{e}_{M} $ and with available experimental data at higher $R{e}_{M} $ . This simplified approach provides a universal criterion to determine the stall angle of stationary thin aerofoils with a parabolic nose.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. Bhaskaran & A. P. Rothmayer 1998 Separation and instabilities in the viscous flow over airfoil leading edges. Comput. Fluids 27 (8), 903921.

L. W. Carr 1988 Progress in analysis and prediction of dynamic stall. J. Aircraft 25 (1), 617.

H. K. Cheng & F. T. Smith 1982 The influence of airfoil thickness and Reynolds number on separation. J. Appl. Math. Phys. (Z. Angew. Math. Phys.) 33, 151180.

L. L. van Dommelen & S. F. Shen 1980 The spontaneous generation of the singularity in a separating laminar boundary layer. J. Comput. Phys. 38 (2), 125140.

R. H. Liebeck 1973 A class of airfoils designed for high lift in incompressible flow. J. Aircraft 10 (10), 610617.

Y. Nakayama 1988 Visualized Flow. Pergamon.

J. Pavelka & K. Tatum 1981 Validation of a wing leading-edge stall prediction technique. J. Aircraft 18 (10), 849854.

J. T. Pinier , J. M. Ausseur , M. N. Glauser & H. Higuchi 2007 Proportional closed-loop feedback control of flow separation. AIAA J. 45 (1), 181190.

E. Sousa 2003 The controversial stability analysis. Appl. Maths Comput. 145 (2/3), 777794.

K. Stewartson , F. T. Smith & K. Kaups 1982 Marginal separation. Stud. Appl. Maths 67 (1), 4561.

V. V. Sychev , A. I. Ruban , V. V. Sychev & G. L. Korolev 1998 Asymptotic Theory of Separated Flows. Cambridge University Press.

I. Tani 1964 Low speed flows involving bubble separations. Prog. Aerosp. Sci. 5, 70103.

H. D. Thompson , B. W. Webb & J. D. Hoffman 1985 The cell Reynolds number myth. Intl J. Numer. Meth. Fluids 5, 305310.

B. E. Webster , M. S. Shephard , Z. Rusak & J. E. Flaherty 1994 Automated adaptive time-discontinuous finite-element method for unsteady compressible aerofoil aerodynamics. AIAA J. 32 (4), 748757.

M. J. Werle & R. T. Davis 1972 Incompressible laminar boundary layers on a parabola at angle of attack: a study of the separation point. Trans. ASME: J. Appl. Mech. 39 (1), 712.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 26 *
Loading metrics...

Abstract views

Total abstract views: 2094 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd May 2017. This data will be updated every 24 hours.